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Springerplus. 2016 Jul 7;5(1):989. doi: 10.1186/s40064-016-2705-4. eCollection 2016.

Groupies in multitype random graphs.

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1
Department of Mathematics, Tongji University, Shanghai, 200092 China.

Abstract

A groupie in a graph is a vertex whose degree is not less than the average degree of its neighbors. Under some mild conditions, we show that the proportion of groupies is very close to 1/2 in multitype random graphs (such as stochastic block models), which include Erdős-Rényi random graphs, random bipartite, and multipartite graphs as special examples. Numerical examples are provided to illustrate the theoretical results.

KEYWORDS:

Degree; Groupie; Multitype; Random graph

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